You hear the stories of Friends of Jaclyn and you realize how little baseball should matter.

Then, you see the smiles on kids who have been dealt some of the worst hands in life and you realize baseball can be much more than just a game.

During their HOPE Week event on Wednesday, the Yankees invited three children to be part of the team, with the help of Friends of Jaclyn, a foundation created to improve the quality of life for pediatric brain tumor patients by connecting them with sports teams.

Ryan Tucker, a 12-year-old who has battled cancer since he was 3, got to live out a lifelong dream by spending the day with his favorite team, along with 11-year-old Sean Callahan and his 4-year-old cousin, Quinn.

They were signed to one-day contracts with the Yankees and given uniforms and lockers, spending time with their new teammates at lunch and on the field.

“I never imagined any of this,” said Tucker. “It’s great. I know I’m having a lot of fun.”

The foundation began because of Jaclyn Murphy, who was diagnosed with a malignant brain tumor in 2004 at age 9 and given a 30 percent chance to live. Soon after, the Northwestern women’s lacrosse team made her an honorary member, and then won its first-ever national championship.

Knowing how much the team’s support meant in his daughter’s recovery, Denis Murphy created the foundation, which has paired over 500 children with teams.

“Everything that they were doing for Jaclyn impacted her health — I know that for a fact,” said Murphy, whose daughter has been cancer-free for nine years. “I realized I had to do that for other kids.”

Early Wednesday morning, Dan Callahan wasn’t sure his son would be allowed to come to The Bronx from the Westchester hospital he had been confined to for the past 40 days.

Ryan Tucker meets Derek Jeter Wednesday in the Yankees clubhouse.

At 10 a.m., Sean, who has undergone four surgeries, including two brain surgeries, was granted permission to join the team, and by 4 p.m., he was sitting at his own locker, calling his family to let them know who was one stall over — Derek Jeter.

“Talk about an overwhelming experience,” said Dan, whose son has been released from the hospital, but will undergo radiation next month. “We’re just happy to be out of the hospital and go back to somewhat of a normal life. To come here, it’s unreal. It’s been great for him. It can’t get any better. Who gets an experience like this?”

Quinn’s father, Tom Ostergren, was able to delay her return to chemotherapy by a day so that she could be part of the experience.

“They’re giants to her,” said Tom. “She knows some of the players from TV and as soon as she saw [Joe Girardi], that’s when it started to become real. … She’s convinced she’s pitching today.”

Pitcher David Robertson spent most of his afternoon with the kids, taking them into the clubhouse and on the field, feeling similarly overwhelmed. It’s hard for him to fathom how much he and the rest of the Yankees can mean.

“The kids are so much fun,” said Robertson. “It’s hard for us because we’re just people too, but it is overwhelming sometimes when you meet children who are so excited to meet you.

“They’re going through some hard times and it’s nice to be able to spend a day with them and put some smiles on their faces.”